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Category: Geometry

Let-P-be-an-interior-point-of-a-triangle-ABC-whose-sidelengths-are-26-65-78-The-line-through-P-parallel-to-BC-meets-AB-in-K-and-AC-in-L-The-line-through-P-parallel-to-CA-meets-BC-in-M-and-BA-in-N-

Question Number 21228 by Tinkutara last updated on 16/Sep/17 $$\mathrm{Let}\:{P}\:\mathrm{be}\:\mathrm{an}\:\mathrm{interior}\:\mathrm{point}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$${ABC}\:\mathrm{whose}\:\mathrm{sidelengths}\:\mathrm{are}\:\mathrm{26},\:\mathrm{65},\:\mathrm{78}. \\ $$$$\mathrm{The}\:\mathrm{line}\:\mathrm{through}\:{P}\:\mathrm{parallel}\:\mathrm{to}\:{BC}\:\mathrm{meets} \\ $$$${AB}\:\mathrm{in}\:{K}\:\mathrm{and}\:{AC}\:\mathrm{in}\:{L}.\:\mathrm{The}\:\mathrm{line}\:\mathrm{through} \\ $$$${P}\:\mathrm{parallel}\:\mathrm{to}\:{CA}\:\mathrm{meets}\:{BC}\:\mathrm{in}\:{M}\:\mathrm{and}\:{BA} \\ $$$$\mathrm{in}\:{N}.\:\mathrm{The}\:\mathrm{line}\:\mathrm{through}\:{P}\:\mathrm{parallel}\:\mathrm{to}\:{AB} \\ $$$$\mathrm{meets}\:{CA}\:\mathrm{in}\:{S}\:\mathrm{and}\:{CB}\:\mathrm{in}\:{T}.\:\mathrm{If}\:{KL},\:{MN}, \\ $$$${ST},\:\mathrm{are}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{lengths},\:\mathrm{find}\:\mathrm{this} \\…

Imtegrate-e-ax-2-bx-c-dx-for-a-gt-0-It-s-just-for-fun-If-you-have-questions-leave-a-comment-I-ll-do-my-best-to-answer-them-

Question Number 20977 by alex041103 last updated on 09/Sep/17 $${Imtegrate}\:\int{e}^{−{ax}^{\mathrm{2}} +{bx}+{c}} {dx}\:{for}\:{a}>\mathrm{0}. \\ $$$${It}'{s}\:{just}\:{for}\:{fun}.\:{If}\:{you}\:{have}\:{questions} \\ $$$${leave}\:{a}\:{comment}.\:{I}'{ll}\:{do}\:{my}\:{best}\:{to}\:{answer}\:{them}. \\ $$ Commented by alex041103 last updated on 10/Sep/17…

Question-151973

Question Number 151973 by ajfour last updated on 24/Aug/21 Commented by ajfour last updated on 24/Aug/21 $${OB}={OC}=\sqrt{{OA}}\:\:;\:{OM}=\mathrm{1} \\ $$$${yellow}\:{area}=\mathrm{1}/\mathrm{4}\:,\:{then}\:{find} \\ $$$${OB}={OC}\:={x}\:\:\:{or}\:\:{OA}={x}^{\mathrm{2}} . \\ $$ Answered…